Evaluate
-\frac{4\sqrt{10}}{75}-0.24\approx -0.408654809
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\int -3x-\sqrt{x}\mathrm{d}x
Evaluate the indefinite integral first.
\int -3x\mathrm{d}x+\int -\sqrt{x}\mathrm{d}x
Integrate the sum term by term.
-3\int x\mathrm{d}x-\int \sqrt{x}\mathrm{d}x
Factor out the constant in each of the terms.
-\frac{3x^{2}}{2}-\int \sqrt{x}\mathrm{d}x
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x\mathrm{d}x with \frac{x^{2}}{2}. Multiply -3 times \frac{x^{2}}{2}.
-\frac{3x^{2}}{2}-\frac{2x^{\frac{3}{2}}}{3}
Rewrite \sqrt{x} as x^{\frac{1}{2}}. Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{\frac{1}{2}}\mathrm{d}x with \frac{x^{\frac{3}{2}}}{\frac{3}{2}}. Simplify. Multiply -1 times \frac{2x^{\frac{3}{2}}}{3}.
-\frac{3}{2}\times 0.4^{2}-\frac{2}{3}\times 0.4^{\frac{3}{2}}-\left(-\frac{3}{2}\times 0^{2}-\frac{2}{3}\times 0^{\frac{3}{2}}\right)
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
-\frac{6}{25}-\frac{4\sqrt{10}}{75}
Simplify.
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